This study is designed to test the hypothesis that paclitaxel (taxol) can be safely administered to children with relapsed leukemia as a continuous 24 hour infusion. The following specific aims will be addressed in this Phase I study to test this hypothesis: 1) to determine the maximum tolerable dose of paclitaxel given as a continuous 24 hour infusion; 2) to determine the toxicities of paclitaxel given on this schedule; and 3) to determine the antileukemic activity of paclitaxel within the confines of a Phase I study.